An ideal turbojet engine is analyzed using the cold air standard method. Given specific operating conditions determine the temperature, pressure, and enthalpy at each state, and the exit velocity. --Given Values--
T1 (K) = 249
P1 (kPa) = 61
V1 (m/s) = 209
rp = 10.7
rc = 1.8

Required:
a. Determine the temperature (K) at state 2.
b. Determine the pressure (kPa) at state 2.
c. Determine the specific enthalpy (kJ/kg) at state 2.
d. Determine the temperature (K) at state 3.

a.  the temperature (K) at state 2 is  

b.  the pressure (kPa) at state 2 is  

c.  the specific enthalpy (kJ/kg) at state 2 is

d.  the temperature (K) at state 3 is  

Explanation:

From the given information:

T1 (K) = 249

P1 (kPa) = 61

V1 (m/s) = 209

rp = 10.7

rc = 1.8

The objective is  to determine the following:

a. Determine the temperature (K) at state 2.

b. Determine the pressure (kPa) at state 2.

c. Determine the specific enthalpy (kJ/kg) at state 2.

d. Determine the temperature (K) at state 3.

To start with the specific enthalpy (kJ/kg) at state 2.

By the relation of steady -flow energy balance equation for diffuser (isentropic)

For ideal gas;enthalpy is only a function of temperature, hence T = h

where;

is the specific enthalpy at inlet  =

is the specific enthalpy at  outlet =

 = 1.004  kJ/kg.K or 1004 J/kg.K

Given that:

(K) = 249

(m/s) = 209

∴

Determine the temperature (K) at state 2.

SInce;

Determine the pressure (kPa) at state 2.

For isentropic condition,

where ;

k = specific heat ratio = 1.4

d. Determine the temperature (K) at state 3.

For the isentropic process

where;

is the compressor ratio

Given that ; the compressor ratio = 10.7